1. Field of the Invention
The present invention relates to a parallel kinematic machine, and a calibration technology of identifying kinematic parameters in the parallel kinematic machine.
2. Description of the Related Art
A parallel kinematic mechanism which is provided with a base and an end effecter connected parallel to each other by plural driver shafts has higher rigidity and accuracy in posturing than a mechanism which is provided with a cantilever. The Stewart platform is a typical example of the parallel kinematic mechanisms. The Stewart platform has straight driver shafts or struts which are expanded or contracted to control the posture including a position and an orientation of an end effecter. For the highly accurate posturing, however, it is necessary to calculate accurate kinematic parameters such as the length of a strut, coordinates of a joint connecting a strut and a base, and a joint connecting a strut and the end effecter. This operation is known as parallel kinematic mechanism calibration, which is studied by various research institutes of the industry, the government, and the academy.
Generally, such calibration requires solution of multiple simultaneous equations whose number is the same as those of the parameters. To this end, it is necessary to place the end effecter in a determined position and a determined orientation, and determine all or a part of position coordinates (X, Y, Z) and orientation coordinates (A, B, C) in the determined state.
Japanese Unexamined Patent Publication No. 2002-91522 discloses a technology whereby the end effecter is moved in a circle in a given posture, and a radial error in the locus of the circular movement is measured by a range meter of a double ball bar (DBB) system, and kinematic parameters are then calculated based on thus-obtained measurement values in order to determine position coordinates and orientation coordinates. Also, Japanese Unexamined Patent Publication No. 2003-200367 discloses a technology that multiple simultaneous equations are separated into eleven or more equations showing relationships between the end effecter position and the kinematic parameters, and one equation showing a relationship between the end effecter orientation and the kinematic parameters, and these equations are solved to calculate kinematic parameters to execute calibration.
Both of the prior art documents, however, employ small scale kinematics to identify kinematic parameters. It is difficult to analytically solve kinematics problems, particularly, forward kinematics problems. The small scale kinematics, which is also called as differential kinematics or displacement kinematics, is one of the academic fields studying an arithmetic approach of solving these problems. In the small scale kinematics, nonlinear equations describing the forward kinematics are differentiated by the respective kinematic parameters to calculate linear expressions that satisfy relations between errors i.e. small scale displacements of kinematic parameters, and errors i.e. small scale displacements of position coordinates so as to analytically solve the linear expressions. In other words, the small scale kinematics deals with a mathematical expression between an error of a certain numerical value, and an error of another numerical value.
However, it can be seen that the former prior art document refers to the fact that at least one kinematic parameter cannot be acquired. Also, the technology of the latter prior art document requires measurement after posturing, and in particular requires at least one measurement in the posture that involves difficult measurement. Also, the small scale kinematics employed in both of the prior art documents has a difficulty in suppressing numerical errors concerning the relational expressions on small scale displacement. Accordingly, in the case where gravity deformation or a like factor is inevitably involved particularly in use of a large-sized machine tool, convergence in numerically identifying kinematic parameters is poor, which obstructs accurate identification of the kinematic parameters.